Recipe

Turn a thermistor reading into degrees

Use when: an NTC thermistor sits on top of a fixed resistor in a divider, read by an analog pin

Goal: the temperature in °C, from the ADC code (or millivolts) and the thermistor's datasheet numbers

Taught in Temperature and humidity

1. 1

   On the Uno R4, use the code itself: ratio = code / 1024. On the ESP32-S3, use analogReadMilliVolts and the 3V3 rail you measured: ratio = mV / supply mV.

   Example

   Uno R4, code 450: ratio = 450 / 1024 = 0.439.

   Why: the divider's output is a fraction of its supply, so the fraction is what carries the information.

2. 2

   With the thermistor on top: R_{NTC} = R_f \times (1 - \text{ratio}) / \text{ratio}.

   Example

   10\ \text{k}\Omega \times (1024 - 450) / 450 = 12{,}756\ \Omega.

   Why: this is the divider formula rearranged for the one unknown resistor.

3. 3

   1/T = 1/298.15 + \ln(R_{NTC}/R_{25})/\beta, then subtract 273.15.

   Example

   \ln(1.2756) = 0.2434; 0.2434 / 3977 = 0.0000612; 1/T = 0.0033540 + 0.0000612 = 0.0034152; T = 292.8 K, about 19.7 °C.

   Why: the beta model is a straight line between 1/T and \ln R, and kelvin starts at true zero.

4. 4

   Find the two table rows either side of your resistance.

   Example

   Vishay lists 15,698 Ω at 15 °C and 12,488 Ω at 20 °C. 12,756 Ω sits between, near 20 °C.

   • your answer falls between them — done.
   • it doesn't — check the divider's orientation and the units (kelvin, ohms).

   Why: an upside-down divider or a forgotten 273.15 gives a wildly wrong answer that a table catches at a glance.